Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #449 |
345 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|c^2=df,d^2=f,b^a=bf,c^a=ce,h^a=h^2,c^b=cd,d^b=df,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5158, D3×#4734, C2×#10590962, … |
| maximal normal subgroup of | D3×#5158, D3×#4734, C2×#10590962, … |
| maximal quotient of | #11778073, #11778186, #11778525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2844);